Slope filtrations of log $p$-divisible groups

TL;DR

This paper extends the concept of slope filtrations from classical $p$-divisible groups to log $p$-divisible groups, broadening the understanding of their structure in logarithmic geometry.

Contribution

It generalizes Oort-Zink's result by establishing slope filtrations for log $p$-divisible groups over normal bases in characteristic $p$.

Findings

Log $p$-divisible groups admit slope filtrations under certain conditions.

The generalization applies to bases with normality in characteristic $p$.

Provides a framework for analyzing the structure of log $p$-divisible groups.

Abstract

Oort-Zink proved that a $p$-divisible group over a normal base in characteristic $p$ with constant Newton polygon is isogenous to a $p$-divisible group admitting a slope filtration. In this paper, we generalize this result to log $p$-divisible groups.